In illumination systems of microlithographic projection exposure apparatus, which are used for the production of finely structured semiconductor components, flat arrangements of beam deviating elements can be used to manipulate the projection light to try to improve the imaging properties of the microlithographic projection exposure apparatus. One example of this involves so-called multi-mirror arrays, in which a multiplicity of micromirrors are arranged in an array, such as in rows and columns. The micromirrors are movable, such as tiltable about two axes provided perpendicularly to one another, so that their surface normal can be tilted into any directions starting from a neutral position. This can allow for variable alterations in the illumination settings in illumination systems.